Problem: Solve for $x$ and $y$ using elimination. ${-2x+4y = 32}$ ${2x-3y = -23}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-2x+4y = 32}\thinspace$ to find $x$ ${-2x + 4}{(9)}{= 32}$ $-2x+36 = 32$ $-2x+36{-36} = 32{-36}$ $-2x = -4$ $\dfrac{-2x}{{-2}} = \dfrac{-4}{{-2}}$ ${x = 2}$ You can also plug ${y = 9}$ into $\thinspace {2x-3y = -23}\thinspace$ and get the same answer for $x$ : ${2x - 3}{(9)}{= -23}$ ${x = 2}$